Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Thermo Fisher.
Tasas de retorno
Thermo Fisher Scientific Inc., tasas mensuales de retorno
| Thermo Fisher Scientific Inc. (TMO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTMO,t1 | DividendoTMO,t1 | RTMO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $245.67 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $259.57 | 5.66% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $273.72 | $0.19 | 5.52% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $277.45 | 1.36% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $495.76 | 11.46% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $530.79 | $0.35 | 7.14% | 4,769.83 | 4.42% |
| Promedio (R): | 1.55% | 1.11% | ||||
| Desviación estándar: | 6.71% | 5.31% | ||||
| Thermo Fisher Scientific Inc. (TMO) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTMO,t1 | DividendoTMO,t1 | RTMO,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $245.67 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $259.57 | 5.66% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $273.72 | $0.19 | 5.52% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $277.45 | 1.36% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $266.98 | -3.77% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $293.68 | $0.19 | 10.07% | 2,941.76 | 6.89% |
| 6. | 31 jul. 2019 | $277.68 | -5.45% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $287.06 | 3.38% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $291.27 | $0.19 | 1.53% | 2,976.74 | 1.72% |
| 9. | 31 oct. 2019 | $301.98 | 3.68% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $313.95 | 3.96% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $324.87 | $0.19 | 3.54% | 3,230.78 | 2.86% |
| 12. | 31 ene. 2020 | $313.19 | -3.60% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $290.80 | -7.15% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $283.60 | $0.22 | -2.40% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $334.68 | 18.01% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $349.19 | 4.34% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $362.34 | $0.22 | 3.83% | 3,100.29 | 1.84% |
| 18. | 31 jul. 2020 | $413.95 | 14.24% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $428.98 | 3.63% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $441.52 | $0.22 | 2.97% | 3,363.00 | -3.92% |
| 21. | 31 oct. 2020 | $473.12 | 7.16% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $464.98 | -1.72% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $465.78 | $0.22 | 0.22% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $509.70 | 9.43% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $450.08 | -11.70% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $456.38 | $0.26 | 1.46% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $470.23 | 3.03% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $469.50 | -0.16% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $504.47 | $0.26 | 7.50% | 4,297.50 | 2.22% |
| 30. | 31 jul. 2021 | $540.01 | 7.05% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $554.95 | 2.77% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $571.33 | $0.26 | 3.00% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $633.07 | 10.81% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $632.83 | -0.04% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $667.24 | $0.26 | 5.48% | 4,766.18 | 4.36% |
| 36. | 31 ene. 2022 | $581.30 | -12.88% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $544.00 | -6.42% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $590.65 | $0.30 | 8.63% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $552.92 | -6.39% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $567.57 | 2.65% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $543.28 | $0.30 | -4.23% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $598.41 | 10.15% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $545.32 | -8.87% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $507.19 | $0.30 | -6.94% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $513.97 | 1.34% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $560.22 | 9.00% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $550.69 | $0.30 | -1.65% | 3,839.50 | -5.90% |
| 48. | 31 ene. 2023 | $570.33 | 3.57% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $541.76 | -5.01% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $576.37 | $0.35 | 6.45% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $554.90 | -3.73% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $508.46 | -8.37% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $521.75 | $0.35 | 2.68% | 4,376.86 | 4.71% |
| 54. | 31 jul. 2023 | $548.66 | 5.16% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $557.10 | 1.54% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $506.17 | $0.35 | -9.08% | 4,288.05 | -4.87% |
| 57. | 31 oct. 2023 | $444.77 | -12.13% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $495.76 | 11.46% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $530.79 | $0.35 | 7.14% | 4,769.83 | 4.42% |
| Promedio (R): | 1.55% | 1.11% | ||||
| Desviación estándar: | 6.71% | 5.31% | ||||
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de TMO durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
Thermo Fisher Scientific Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RTMO,t | RS&P 500,t | (RTMO,t–RTMO)2 | (RS&P 500,t–RS&P 500)2 | (RTMO,t–RTMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 5.66% | 2.97% | 16.84 | 3.49 | 7.66 |
| 2. | 31 mar. 2019 | 5.52% | 1.79% | 15.76 | 0.47 | 2.73 |
| 3. | 30 abr. 2019 | 1.36% | 3.93% | 0.04 | 7.98 | -0.54 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | 11.46% | 8.92% | 98.20 | 61.03 | 77.41 |
| 59. | 31 dic. 2023 | 7.14% | 4.42% | 31.16 | 11.00 | 18.51 |
| Total (Σ): | 2,609.92 | 1,634.30 | 1,315.98 | |||
| t | Fecha | RTMO,t | RS&P 500,t | (RTMO,t–RTMO)2 | (RS&P 500,t–RS&P 500)2 | (RTMO,t–RTMO)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 5.66% | 2.97% | 16.84 | 3.49 | 7.66 |
| 2. | 31 mar. 2019 | 5.52% | 1.79% | 15.76 | 0.47 | 2.73 |
| 3. | 30 abr. 2019 | 1.36% | 3.93% | 0.04 | 7.98 | -0.54 |
| 4. | 31 may. 2019 | -3.77% | -6.58% | 28.39 | 59.04 | 40.94 |
| 5. | 30 jun. 2019 | 10.07% | 6.89% | 72.54 | 33.49 | 49.29 |
| 6. | 31 jul. 2019 | -5.45% | 1.31% | 49.04 | 0.04 | -1.45 |
| 7. | 31 ago. 2019 | 3.38% | -1.81% | 3.32 | 8.50 | -5.31 |
| 8. | 30 sept. 2019 | 1.53% | 1.72% | 0.00 | 0.37 | -0.01 |
| 9. | 31 oct. 2019 | 3.68% | 2.04% | 4.50 | 0.88 | 1.99 |
| 10. | 30 nov. 2019 | 3.96% | 3.40% | 5.80 | 5.28 | 5.54 |
| 11. | 31 dic. 2019 | 3.54% | 2.86% | 3.94 | 3.07 | 3.48 |
| 12. | 31 ene. 2020 | -3.60% | -0.16% | 26.52 | 1.61 | 6.53 |
| 13. | 29 feb. 2020 | -7.15% | -8.41% | 75.76 | 90.57 | 82.83 |
| 14. | 31 mar. 2020 | -2.40% | -12.51% | 15.64 | 185.44 | 53.86 |
| 15. | 30 abr. 2020 | 18.01% | 12.68% | 270.82 | 134.06 | 190.54 |
| 16. | 31 may. 2020 | 4.34% | 4.53% | 7.73 | 11.71 | 9.52 |
| 17. | 30 jun. 2020 | 3.83% | 1.84% | 5.17 | 0.54 | 1.67 |
| 18. | 31 jul. 2020 | 14.24% | 5.51% | 161.00 | 19.40 | 55.88 |
| 19. | 31 ago. 2020 | 3.63% | 7.01% | 4.31 | 34.82 | 12.25 |
| 20. | 30 sept. 2020 | 2.97% | -3.92% | 2.02 | 25.29 | -7.14 |
| 21. | 31 oct. 2020 | 7.16% | -2.77% | 31.39 | 15.00 | -21.69 |
| 22. | 30 nov. 2020 | -1.72% | 10.75% | 10.73 | 93.10 | -31.60 |
| 23. | 31 dic. 2020 | 0.22% | 3.71% | 1.78 | 6.79 | -3.48 |
| 24. | 31 ene. 2021 | 9.43% | -1.11% | 62.01 | 4.93 | -17.48 |
| 25. | 28 feb. 2021 | -11.70% | 2.61% | 175.61 | 2.26 | -19.92 |
| 26. | 31 mar. 2021 | 1.46% | 4.24% | 0.01 | 9.85 | -0.31 |
| 27. | 30 abr. 2021 | 3.03% | 5.24% | 2.19 | 17.11 | 6.12 |
| 28. | 31 may. 2021 | -0.16% | 0.55% | 2.92 | 0.31 | 0.95 |
| 29. | 30 jun. 2021 | 7.50% | 2.22% | 35.39 | 1.24 | 6.64 |
| 30. | 31 jul. 2021 | 7.05% | 2.27% | 30.14 | 1.37 | 6.42 |
| 31. | 31 ago. 2021 | 2.77% | 2.90% | 1.47 | 3.22 | 2.17 |
| 32. | 30 sept. 2021 | 3.00% | -4.76% | 2.08 | 34.37 | -8.46 |
| 33. | 31 oct. 2021 | 10.81% | 6.91% | 85.59 | 33.74 | 53.74 |
| 34. | 30 nov. 2021 | -0.04% | -0.83% | 2.54 | 3.76 | 3.09 |
| 35. | 31 dic. 2021 | 5.48% | 4.36% | 15.40 | 10.60 | 12.77 |
| 36. | 31 ene. 2022 | -12.88% | -5.26% | 208.36 | 40.51 | 91.87 |
| 37. | 28 feb. 2022 | -6.42% | -3.14% | 63.54 | 17.99 | 33.81 |
| 38. | 31 mar. 2022 | 8.63% | 3.58% | 50.07 | 6.11 | 17.49 |
| 39. | 30 abr. 2022 | -6.39% | -8.80% | 63.09 | 98.04 | 78.64 |
| 40. | 31 may. 2022 | 2.65% | 0.01% | 1.20 | 1.21 | -1.20 |
| 41. | 30 jun. 2022 | -4.23% | -8.39% | 33.43 | 90.21 | 54.91 |
| 42. | 31 jul. 2022 | 10.15% | 9.11% | 73.84 | 64.09 | 68.79 |
| 43. | 31 ago. 2022 | -8.87% | -4.24% | 108.71 | 28.62 | 55.78 |
| 44. | 30 sept. 2022 | -6.94% | -9.34% | 72.11 | 109.11 | 88.70 |
| 45. | 31 oct. 2022 | 1.34% | 7.99% | 0.05 | 47.34 | -1.50 |
| 46. | 30 nov. 2022 | 9.00% | 5.38% | 55.41 | 18.23 | 31.78 |
| 47. | 31 dic. 2022 | -1.65% | -5.90% | 10.26 | 49.04 | 22.43 |
| 48. | 31 ene. 2023 | 3.57% | 6.18% | 4.05 | 25.70 | 10.20 |
| 49. | 28 feb. 2023 | -5.01% | -2.61% | 43.09 | 13.82 | 24.40 |
| 50. | 31 mar. 2023 | 6.45% | 3.51% | 23.99 | 5.76 | 11.75 |
| 51. | 30 abr. 2023 | -3.73% | 1.46% | 27.88 | 0.13 | -1.89 |
| 52. | 31 may. 2023 | -8.37% | 0.25% | 98.48 | 0.74 | 8.51 |
| 53. | 30 jun. 2023 | 2.68% | 4.71% | 1.27 | 13.02 | 4.07 |
| 54. | 31 jul. 2023 | 5.16% | 4.85% | 12.98 | 13.99 | 13.47 |
| 55. | 31 ago. 2023 | 1.54% | -1.77% | 0.00 | 8.28 | 0.05 |
| 56. | 30 sept. 2023 | -9.08% | -4.87% | 113.08 | 35.73 | 63.57 |
| 57. | 31 oct. 2023 | -12.13% | -2.20% | 187.28 | 10.92 | 45.21 |
| 58. | 30 nov. 2023 | 11.46% | 8.92% | 98.20 | 61.03 | 77.41 |
| 59. | 31 dic. 2023 | 7.14% | 4.42% | 31.16 | 11.00 | 18.51 |
| Total (Σ): | 2,609.92 | 1,634.30 | 1,315.98 | |||
Mostrar todo
VarianzaTMO = Σ(RTMO,t–RTMO)2 ÷ (59 – 1)
= 2,609.92 ÷ (59 – 1)
= 45.00
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaTMO, S&P 500 = Σ(RTMO,t–RTMO)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,315.98 ÷ (59 – 1)
= 22.69
Estimación sistemática del riesgo (β)
| VarianzaTMO | 45.00 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaTMO, S&P 500 | 22.69 |
| Coeficiente de correlaciónTMO, S&P 5001 | 0.64 |
| βTMO2 | 0.81 |
| αTMO3 | 0.66% |
Cálculos
1 Coeficiente de correlaciónTMO, S&P 500
= CovarianzaTMO, S&P 500 ÷ (Desviación estándarTMO × Desviación estándarS&P 500)
= 22.69 ÷ (6.71% × 5.31%)
= 0.64
2 βTMO
= CovarianzaTMO, S&P 500 ÷ VarianzaS&P 500
= 22.69 ÷ 28.18
= 0.81
3 αTMO
= PromedioTMO – βTMO × PromedioS&P 500
= 1.55% – 0.81 × 1.11%
= 0.66%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Thermo Fisher acciones ordinarias | βTMO | 0.81 |
| Tasa de rentabilidad esperada de las acciones ordinarias de Thermo Fisher3 | E(RTMO) | 12.01% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(RTMO) = RF + βTMO [E(RM) – RF]
= 4.65% + 0.81 [13.79% – 4.65%]
= 12.01%